Limited accuracy of conduction band effective mass equations for semiconductor quantum dots
Abstract Effective mass equations are the simplest models of carrier states in a semiconductor structures that reduce the complexity of a solid-state system to Schrödinger- or Pauli-like equations resempling those well known from quantum mechanics textbooks. Here we present a systematic derivation o...
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| Main Authors: | , , |
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| Format: | article |
| Language: | EN |
| Published: |
Nature Portfolio
2018
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| Subjects: | |
| Online Access: | https://doaj.org/article/db52853d41b247679ebfc2acbdcdf744 |
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| Summary: | Abstract Effective mass equations are the simplest models of carrier states in a semiconductor structures that reduce the complexity of a solid-state system to Schrödinger- or Pauli-like equations resempling those well known from quantum mechanics textbooks. Here we present a systematic derivation of a conduction-band effective mass equation for a self-assembled semiconductor quantum dot in a magnetic field from the 8-band k · p theory. The derivation allows us to classify various forms of the effective mass equations in terms of a hierarchy of approximations. We assess the accuracy of the approximations in calculating selected spectral and spin-related characteristics. We indicate the importance of preserving the off-diagonal terms of the valence band Hamiltonian and argue that an effective mass theory cannot reach satisfactory accuracy without self-consistently including non-parabolicity corrections and renormalization of k · p parameters. Quantitative comparison with the 8-band k · p results supports the phenomenological Roth-Lax-Zwerdling formula for the g-factor in a nanostructure. |
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